2ο ΜΕΡΟΣ: Ανίχνευση Σημείων Ενδιαφέροντος¶
In [1]:
#Απαραίτητες Βιβλιοθήκες
from IPython.display import Image
import cv2
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from scipy import ndimage, misc
import math
import sys
from matplotlib.patches import Circle
Έτοιμες Συναρτήσεις:¶
In [2]:
def interest_points_visualization(I_, kp_data_,title,ax=None):
'''
Plot keypoints chosen by detectos on image.
Args:
I_: Image (if colored, make sure it is in RGB and not BGR).
kp_data_: Nx3 array, as described in assignment.
ax: Matplotlib axis to plot on (if None, a new Axes object is created).
Returns:
ax: Matplotlib axis where the image was plotted.
'''
try:
I = np.array(I_)
kp_data = np.array(kp_data_)
except:
print('Conversion to numpy arrays failed, check if the inputs (image and keypoints) are in the required format.')
exit(2)
try:
assert(len(I.shape) == 2 or (len(I.shape) == 3 and I.shape[2] == 3))
except AssertionError as e:
print('interest_points_visualization: Image must be either a 2D matrix or a 3D matrix with the last dimension having size equal to 3.', file=sys.stderr)
exit(2)
try:
assert(len(kp_data.shape) == 2 and kp_data.shape[1] == 3)
except AssertionError as e:
print('interest_points_visualization: kp_data must be a 2D matrix with 3 columns.', file=sys.stderr)
exit(2)
if ax is None:
_, ax = plt.subplots(figsize=(20, 10))
ax.set_aspect('equal')
ax.set_title(title, fontsize=20)
ax.imshow(I)
ax.tick_params(bottom=False, left=False, labelbottom=False, labelleft=False)
for i in range(len(kp_data)):
x, y, sigma = kp_data[i]
circ = Circle((x, y), 3*sigma, edgecolor='g', fill=False, linewidth=2)
ax.add_patch(circ)
return ax
In [3]:
def disk_strel(n):
'''
Return a structural element, which is a disk of radius n.
'''
r = int(np.round(n))
d = 2*r+1
x = np.arange(d) - r
y = np.arange(d) - r
x, y = np.meshgrid(x,y)
strel = x**2 + y**2 <= r**2
return strel.astype(np.uint8)
Ανάγνωση - Κανονικοποίηση - Εμφάνιση Εικόνας¶
In [4]:
#n_img1: Κανονικοποιημένη Ασπρόμαυρη Εικόνα
img1 = cv2.imread('Caravaggio2.jpg',cv2.IMREAD_GRAYSCALE)
n_img1 = img1.astype(np.float)/255
#n_img2: Κανονικοποιημένη Έγχρωμη Εικόνα
img2 = cv2.imread('Caravaggio2.jpg')
img2 = cv2.cvtColor(img2,cv2.COLOR_BGR2RGB)
n_img2 = cv2.normalize(img2.astype('float'), None, 0.0, 1.0, cv2.NORM_MINMAX)
In [5]:
#Εμφάνιση Εικόνων
f, (ax0,ax1) = plt.subplots(1, 2, figsize=(20, 10))
ax0.imshow(n_img1,cmap='gray')
ax0.set_title("Aσπρόμαυρη Εικόνα" , fontsize=20)
ax1.imshow(n_img2,cmap='gray')
ax1.set_title("Έγχρωμη Εικόνα" , fontsize=20)
Out[5]:
2.1. Ανίχνευση Γωνιών¶
In [6]:
#Εξομάλυνση εικόνας
s =2
r= 2.5
ns = int(2*np.ceil(3*s)+1)
rs = int(2*np.ceil(3*r)+1)
gauss1Ds = cv2.getGaussianKernel(ns, s) # Column vector
gauss2Ds = gauss1Ds @ gauss1Ds.T # Symmetric gaussian kernel
gauss1Dr = cv2.getGaussianKernel(rs, r) # Column vector
gauss2Dr = gauss1Dr @ gauss1Dr.T # Symmetric gaussian kernel
Is_1 = cv2.filter2D(n_img1, -1, gauss2Ds)
f, (ax0) = plt.subplots(1, 1, figsize=(20, 10))
ax0.imshow(Is_1 ,cmap='gray')
ax0.set_title("Eξομάλυνση Εικόνας" , fontsize=20)
Out[6]:
2.1.1. Υπολογίσμός J1, J2 και J3¶
In [7]:
[dx,dy] = np.gradient(Is_1)
#2.1.1 Υπολογισμος J
dxdx=np.multiply(dx,dx)
dxdy=np.multiply(dx,dy)
dydy=np.multiply(dy,dy)
J1 = cv2.filter2D(dxdx, -1, gauss2Dr)
J2 = cv2.filter2D(dxdy, -1, gauss2Dr)
J3 = cv2.filter2D(dydy, -1, gauss2Dr)
2.1.2. Υπολογισμός Ιδιοτιμών Τανυστή J¶
In [8]:
# 2.1.2 Υπολογισμός λ1,λ2
J1minusJ3sq = np.multiply((J1-J3),(J1-J3))
J2sq = np.multiply(J2,J2)
lplus = 0.5*(J1 + J3 + np.sqrt(J1minusJ3sq + 4*J2sq));
lminus = 0.5*(J1 + J3 - np.sqrt(J1minusJ3sq + 4*J2sq));
f, (ax0,ax1) = plt.subplots(1, 2, figsize=(20, 10))
ax0.imshow(np.real(lplus),cmap='gray')
ax0.set_title("Θετικές Ιδιοτιμές (λ+)" , fontsize=20)
ax1.imshow(np.real(lminus),cmap='gray')
ax1.set_title("Αρνητικές Ιδιοτιμές (λ-)" , fontsize=20)
Out[8]:
2.1.3. Κριτήριο Γωνιότητας R¶
In [9]:
k = 0.05
R = np.multiply(lplus,lminus)-k*np.multiply(lplus+lminus,lplus+lminus)
#Συνθήκη 1
ns = np.ceil(3*s)*2+1
B_sq = disk_strel(ns)
Cond1 = (R==cv2.dilate(R,B_sq))
Cond1=Cond1*1
#Συνθήκη 2
thetacorn = 0.005;
maxR=np.amax(R)
Cond2 = ( R >= thetacorn*maxR);
Cond2=Cond2*1
y1,x1 = np.where(Cond1 & Cond2)
array_sc = np.ones(y1.shape[0])
param = np.column_stack([x1,y1,array_sc])
In [10]:
interest_points_visualization(n_img2,param,"Μια κλίμακα με Harris-Stephens")
Out[10]:
2.2 Πολυκλιμακωτή Ανίχνευση Γωνιών¶
2.2.1 Eύρεση γωνιών μονής κλίμακας για διαφορετικές κλίμακες¶
In [11]:
#Όλα τα παραπάνω ομαδοποιούνται σε μια συνάρτηση
def harris_laplacian_for_one_scale(I,s,r,k):
ns = int(2*np.ceil(3*s)+1)
rs = int(2*np.ceil(3*r)+1)
gauss1Ds = cv2.getGaussianKernel(ns, s)
gauss2Ds = gauss1Ds @ gauss1Ds.T
gauss1Dr = cv2.getGaussianKernel(rs, r)
gauss2Dr = gauss1Dr @ gauss1Dr.T
Is_1 = cv2.filter2D(n_img1, -1, gauss2Ds)
[dx,dy] = np.gradient(Is_1)
dxdx=np.multiply(dx,dx)
dxdy=np.multiply(dx,dy)
dydy=np.multiply(dy,dy)
J1 = cv2.filter2D(dxdx, -1, gauss2Dr)
J2 = cv2.filter2D(dxdy, -1, gauss2Dr)
J3 = cv2.filter2D(dydy, -1, gauss2Dr)
J1minusJ3sq = np.multiply((J1-J3),(J1-J3))
J2sq = np.multiply(J2,J2)
lplus = 0.5*(J1 + J3 + np.sqrt(J1minusJ3sq + 4*J2sq))
lminus = 0.5*(J1 + J3 - np.sqrt(J1minusJ3sq + 4*J2sq))
R = np.multiply(lplus,lminus)-k*np.multiply(lplus+lminus,lplus+lminus)
#Συνθήκη 1
ns = np.ceil(3*s)*2+1
B_sq = disk_strel(ns)
Cond1 = (R==cv2.dilate(R,B_sq))
Cond1=Cond1*1
#Συνθήκη 2
thetacorn = 0.005;
maxR=np.amax(R)
Cond2 = ( R >= thetacorn*maxR);
Cond2=Cond2*1
y1,x1 = np.where(Cond1 & Cond2)
array_sc = np.ones(y1.shape[0])
param = np.column_stack([x1,y1,array_sc])
return param
2.2.2. Πολυκλιμακωτή Ανίχνευση Γωνιών (Harris-Laplacian)¶
In [12]:
#LoG για διάφορες κλίμακες
def compute_Log(N,s0,scale,I):
AbsLog = np.zeros((I.shape[0],I.shape[1],N))
for K in range(N):
s=s0*scale**(K)
Log_I = ndimage.gaussian_laplace(I,s)
AbsLog[:,:,K] = s*s * abs(Log_I)
return AbsLog
In [13]:
#2.2. Πολυκλιμακωτή Ανίχνευση Γωνιών
s0=2;
r0=2.5;
k=0.05;
thetacorn = 0.005;
scale=1.5;
N=4;
AbsLog = compute_Log(N,s0,scale,n_img1);
for i in range(N):
s=s0*scale**i;
r=r0*scale**i;
ns = int(2*np.ceil(3*s)+1)
rs = int(2*np.ceil(3*r)+1)
gauss1Ds = cv2.getGaussianKernel(ns, s) # Column vector
gauss2Ds = gauss1Ds @ gauss1Ds.T # Symmetric gaussian kernel
gauss1Dr = cv2.getGaussianKernel(rs, r) # Column vector
gauss2Dr = gauss1Dr @ gauss1Dr.T # Symmetric gaussian kernel
Is_1 = cv2.filter2D(n_img1, -1, gauss2Ds)
[dx,dy] = np.gradient(Is_1)
dxdx=np.multiply(dx,dx)
dxdy=np.multiply(dx,dy)
dydy=np.multiply(dy,dy)
J1 = cv2.filter2D(dxdx, -1, gauss2Dr)
J2 = cv2.filter2D(dxdy, -1, gauss2Dr)
J3 = cv2.filter2D(dydy, -1, gauss2Dr)
J1minusJ3sq = np.multiply((J1-J3),(J1-J3))
J2sq = np.multiply(J2,J2)
lplus = 0.5*(J1 + J3 + np.sqrt(J1minusJ3sq + 4*J2sq));
lminus = 0.5*(J1 + J3 - np.sqrt(J1minusJ3sq + 4*J2sq));
R = np.multiply(lplus,lminus)-k*np.multiply(lplus+lminus,lplus+lminus)
ns = np.ceil(3*s)*2+1
B_sq = disk_strel(ns)
Cond1 = (R==cv2.dilate(R,B_sq))
Cond1=Cond1*1
maxR=np.amax(R)
Cond2 = ( R >= thetacorn*maxR);
Cond2=Cond2*1
if (i==0):
AbsLogCond = AbsLog[:,:,i] >= AbsLog[:,:,i+1]
elif (i==N-1):
AbsLogCond= AbsLog[:,:,i] >= AbsLog[:,:,i-1]
else:
AbsLogCond = (AbsLog[:,:,i] >= AbsLog[:,:,i+1])& (AbsLog[:,:,i] >= AbsLog[:,:,i-1])
temp_y,temp_x = np.where(Cond1 & Cond2 & AbsLogCond)
a=temp_x.shape[0]
#print(a)
temp = np.ones((a))*s
Temp_Parameters= np.concatenate((temp_x, temp_y,temp), axis=0)
Temp_Parameters= np.reshape(Temp_Parameters,(3,a))
Temp_Parameters= np.transpose(Temp_Parameters)
if (i==0):
Parameters = Temp_Parameters
else:
Parameters = np.concatenate((Temp_Parameters,Parameters), axis=0)
In [14]:
interest_points_visualization(n_img2,Parameters,"Πολυκλιμακωτή με Harris-Laplacian")
Out[14]:
2.3 Ανίχνευση Blobs¶
2.3.1. Υπολογίσμός Μερικών Παραγώγων Δεύτερης Τάξης της Εικόνας¶
In [15]:
def hessian_criterion(I,s):
ns = int(2*np.ceil(3*s)+1)
n_img1=I
gauss1Ds = cv2.getGaussianKernel(ns, s) # Column vector
gauss2Ds = gauss1Ds @ gauss1Ds.T # Symmetric gaussian kernel
Is_1 = cv2.filter2D(n_img1, -1, gauss2Ds)
[dx,dy] = np.gradient(Is_1)
[hxx,hxy]=np.gradient(dx)
[hxy,hyy]=np.gradient(dy)
R = np.multiply(hxx,hyy)-np.multiply(hxy,hxy)
return R
In [16]:
R1= hessian_criterion(n_img1,2.2)
R2= hessian_criterion(n_img1,5.2)
R3= hessian_criterion(n_img1,9.2)
f, (ax0,ax1,ax2) = plt.subplots(1, 3, figsize=(20, 10))
f.suptitle('Οπτικοποίηση κριτηρίου R για διάφορα scales (Hessian Criterion)',fontsize=30)
ax0.imshow(R1,cmap='gray')
ax0.set_title("scale = 2 ",fontsize=20)
ax1.imshow(R2,cmap='gray')
ax1.set_title("scale = 5" , fontsize=20)
ax2.imshow(R3,cmap='gray')
ax2.set_title("scale = 9" , fontsize=20)
Out[16]:
2.3.2. Επιλογή Σημείων Ενδιαφέροντος¶
In [17]:
s =2
ns = int(2*np.ceil(3*s)+1)
gauss1Ds = cv2.getGaussianKernel(ns, s) # Column vector
gauss2Ds = gauss1Ds @ gauss1Ds.T # Symmetric gaussian kernel
Is_1 = cv2.filter2D(n_img1, -1, gauss2Ds)
[dx,dy] = np.gradient(Is_1)
[hxx,hxy]=np.gradient(dx)
[hxy,hyy]=np.gradient(dy)
R = np.multiply(hxx,hyy)-np.multiply(hxy,hxy)
B_sq = disk_strel(ns);
maxima = (R==cv2.dilate(R,B_sq))
Rmax = np.amax(R)
threshold = 0.07
temp_y,temp_x = np.where(maxima & (R>= (threshold * Rmax)))
array_sc = np.ones(temp_y.shape[0])*s
param = np.column_stack([temp_x,temp_y,array_sc])
In [18]:
interest_points_visualization(n_img2,param,"Blobs με μια κλίμακα")
Out[18]:
2.4 Πολυκλιμακωτή Ανίχνευση Blobs¶
2.4.1 Πολυκλιμακωτή Ανίχνευση Γωνιών (Blobs)¶
In [19]:
#Καθορισμός Παραμέτρων
N=4;
s0=s;
scale=1.85;
threshold = 0.07;
AbsLog = compute_Log( N, s0,scale ,n_img1)
In [20]:
for i in range(N):
s=s0*scale**i
ns = int(2*np.ceil(3*s)+1)
gauss1Ds = cv2.getGaussianKernel(ns, s) # Column vector
gauss2Ds = gauss1Ds @ gauss1Ds.T # Symmetric gaussian kernel
Is_1 = cv2.filter2D(n_img1, -1, gauss2Ds)
[dx,dy] = np.gradient(Is_1)
[hxx,hxy]=np.gradient(dx)
[hxy,hyy]=np.gradient(dy)
R = np.multiply(hxx,hyy)-np.multiply(hxy,hxy)
B_sq = disk_strel(ns);
maxima = (R==cv2.dilate(R,B_sq))
Rmax = np.amax(R)
if (i==0):
AbsLogCond = AbsLog[:,:,i] >= AbsLog[:,:,i+1]
elif (i==N-1):
AbsLogCond= AbsLog[:,:,i] >= AbsLog[:,:,i-1]
else:
AbsLogCond = (AbsLog[:,:,i] >= AbsLog[:,:,i+1])& (AbsLog[:,:,i] >= AbsLog[:,:,i-1])
temp_y,temp_x = np.where(maxima & (R>= (threshold * Rmax)) & AbsLogCond)
a=temp_x.shape[0]
#print(a)
temp = np.ones((a))*s
Temp_Parameters= np.concatenate((temp_x, temp_y,temp), axis=0)
Temp_Parameters= np.reshape(Temp_Parameters,(3,a))
Temp_Parameters= np.transpose(Temp_Parameters)
if (i==0):
Parameters = Temp_Parameters
else:
Parameters = np.concatenate((Temp_Parameters,Parameters), axis=0)
In [21]:
interest_points_visualization(n_img2,Parameters,"Blobs με πολλές κλίμακες")
Out[21]:
2.5.1. Υπολογισμός Ολοκληρωτικής Εικόνας¶
In [22]:
s=2
n=np.ceil(3*s)*2+1
Ipad=np.pad(n_img1,(math.floor(n/2),math.floor(n/2)),'edge')
integral_image=cv2.integral(Ipad)
f, (ax0) = plt.subplots(1, 1, figsize=(10, 5))
ax0.imshow(integral_image)
ax0.set_title("Oλοκληρωική εικόνα μετά απο edge-replicate padding" , fontsize=20)
Out[22]:
In [23]:
def computeSs_Integral(intI, shiftX, shiftY, offsetx, offsety):
sD = np.roll(intI,-shiftY + offsety,0)
sD = np.roll(sD,-shiftX + offsetx,1)
#Left-Top Corner
sA = np.roll(intI,shiftY + offsety,0)
sA = np.roll(sA,shiftX + offsetx,1)
#Right-Top corner
sB = np.roll(intI,shiftY + offsety,0)
sB = np.roll(sB,-shiftX + offsetx,1)
#Left-Bottom Corner
sC = np.roll(intI,-shiftY + offsety,0)
sC = np.roll(sC,shiftX + offsetx,1)
return [sA,sB,sC,sD]
In [24]:
def unpad ( temp_s , pad ):
sx = temp_s.shape[0]
sy = temp_s.shape[1]
s = temp_s[pad:sx - pad+1,pad:sy - pad+1]
return s
2.5.2 Υπολογισμός των Lxx, Lxy, Lyy με χρήση της Ολοκληρωτικής Εικόνας¶
In [25]:
def box_filters_one_scale(I,s):
thresh=0.912
threshold = 0.07
#threshold = 0.02
n = np.ceil(3*s)*2+1
xDxx = 2*math.floor(n/6) + 1
yDxx = 4*math.floor(n/6) + 1
rDxx = math.floor((n-yDxx)/2)
xDyy = 4*math.floor(n/6) + 1
yDyy = 2*math.floor(n/6) + 1
xDxy = 2*math.floor(n/6)+1
yDxy = 2*math.floor(n/6)+1
rDxy =math.floor((n - xDxy - yDxy)/3)
sDxy = math.floor((n - xDxy - yDxy)/3)
mDxy = np.ceil((n - xDxy - yDxy)/3)
if(sDxy + sDxy + mDxy != n-xDxy - yDxy):
sDxy = np.ceil((n - xDxy - yDxy)/3)
mDxy = math.floor((n - xDxy - yDxy)/3)
Ipadded=np.pad(n_img1,(math.floor(n/2),math.floor(n/2)),'edge')
intI=cv2.integral(Ipadded)
#Central Box
magn = -3
shiftX = (xDxx -1)//2
shiftY = (yDxx -1)//2
pad = math.floor(n/2) + 1
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY , 0, 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxx = (sD + sA - sB - sC) * magn
#Left and Right Box
magn = 1
shiftX = (xDxx -1)//2 + xDxx
shiftY = (yDxx -1)//2
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY ,0, 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxx = (sD + sA - sB - sC) * magn + Lxx
# Lyy
#Central Box
magn = -3
shiftX = (xDyy -1)//2
shiftY = (yDyy -1)//2
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY ,0, 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad);
Lyy = (sD + sA - sB - sC) * magn
#Top and Bottom Box
magn = 1;
shiftX = (xDyy -1)//2
shiftY = (yDyy -1)//2 + yDyy
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY , 0 , 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lyy = (sD + sA - sB - sC) * magn + Lyy
if(( math.floor(np.ceil((n-2*xDxy)/3) % 2)) == 1):
rDxy = np.ceil((n-2*xDxy)/3)
else:
rDxy = math.floor((n-2*xDxy)/3)
# Lxy
#Top Right Box
magn = -1
offsetx = - math.floor((rDxy-1)/2) - math.floor((xDxy -1)/2)
offsety = math.floor((rDxy-1)/2) + math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn
#Top Left Box
magn = 1
offsetx = math.floor((rDxy-1)/2) + math.floor((xDxy -1)/2)
offsety = math.floor((rDxy-1)/2) + math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn + Lxy
#Bottom Left Box
magn = -1
offsetx = math.floor((rDxy-1)/2) + math.floor((xDxy -1)/2)
offsety = - math.floor((rDxy-1)/2) - math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn + Lxy
#Bottom Right Box
magn = 1;
offsetx = - math.floor((rDxy-1)/2) - math.floor((xDxy -1)/2)
offsety = - math.floor((rDxy-1)/2) - math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn + Lxy
R=np.multiply(Lxx,Lyy) - np.power((thresh*Lxy),2)
#Finds maxima
ns=np.ceil(3*s)*2+1
B_sq = disk_strel(ns)
maxima = (R==cv2.dilate(R,B_sq))
Rmax = np.amax(R)
interest_map = (maxima & (R >= threshold * Rmax))
return interest_map
2.5.4 Πολυκλιμακωτή Ανίχνευση Γωνιών (Box Filters)¶
In [26]:
N = 4;
s0 = 2.5;
scale = 1.78;
AbsLog = compute_Log(N, s0,scale ,n_img1)
for i in range(4):
s = s0 * scale**i
interest_map=box_filters_one_scale(n_img1,s)
if (i==0):
AbsLogCond = AbsLog[:,:,i] >= AbsLog[:,:,i+1]
elif (i==3):
AbsLogCond= AbsLog[:,:,i] >= AbsLog[:,:,i-1]
else:
AbsLogCond = (AbsLog[:,:,i] >= AbsLog[:,:,i+1])& (AbsLog[:,:,i] >= AbsLog[:,:,i-1])
temp_y,temp_x = np.where(interest_map & AbsLogCond)
a=temp_x.shape[0]
#print(a)
temp = np.ones((a))*s
Temp_Parameters= np.concatenate((temp_x, temp_y,temp), axis=0)
Temp_Parameters= np.reshape(Temp_Parameters,(3,a))
Temp_Parameters= np.transpose(Temp_Parameters)
if (i==0):
Parameters = Temp_Parameters
else:
Parameters = np.concatenate((Temp_Parameters,Parameters), axis=0)
print(Parameters.shape)
In [27]:
interest_points_visualization(n_img2,Parameters,"Πολυκλιμακωτή με Box Filters")
Out[27]:
2.5.3 Οπτικοποίηση Κριτηρίου R¶
In [28]:
def box_filters_criterion(I,s):
n = np.ceil(3*s)*2+1
thresh=0.912
n_img1=I
xDxx = 2*math.floor(n/6) + 1
yDxx = 4*math.floor(n/6) + 1
rDxx = math.floor((n-yDxx)/2)
xDyy = 4*math.floor(n/6) + 1
yDyy = 2*math.floor(n/6) + 1
xDxy = 2*math.floor(n/6)+1
yDxy = 2*math.floor(n/6)+1
rDxy =math.floor((n - xDxy - yDxy)/3)
sDxy = math.floor((n - xDxy - yDxy)/3)
mDxy = np.ceil((n - xDxy - yDxy)/3)
if(sDxy + sDxy + mDxy != n-xDxy - yDxy):
sDxy = np.ceil((n - xDxy - yDxy)/3)
mDxy = math.floor((n - xDxy - yDxy)/3)
Ipadded=np.pad(n_img1,(math.floor(n/2),math.floor(n/2)),'edge')
intI=cv2.integral(Ipadded)
#Central Box
magn = -3
shiftX = (xDxx -1)//2
shiftY = (yDxx -1)//2
pad = math.floor(n/2) + 1
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY , 0, 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxx = (sD + sA - sB - sC) * magn
#Left and Right Box
magn = 1
shiftX = (xDxx -1)//2 + xDxx
shiftY = (yDxx -1)//2
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY ,0, 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxx = (sD + sA - sB - sC) * magn + Lxx
# Lyy
#Central Box
magn = -3
shiftX = (xDyy -1)//2
shiftY = (yDyy -1)//2
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY ,0, 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad);
Lyy = (sD + sA - sB - sC) * magn
#Top and Bottom Box
magn = 1;
shiftX = (xDyy -1)//2
shiftY = (yDyy -1)//2 + yDyy
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY , 0 , 0)
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lyy = (sD + sA - sB - sC) * magn + Lyy
if(( math.floor(np.ceil((n-2*xDxy)/3) % 2)) == 1):
rDxy = np.ceil((n-2*xDxy)/3)
else:
rDxy = math.floor((n-2*xDxy)/3)
# Lxy
#Top Right Box
magn = -1
offsetx = - math.floor((rDxy-1)/2) - math.floor((xDxy -1)/2)
offsety = math.floor((rDxy-1)/2) + math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn
#Top Left Box
magn = 1
offsetx = math.floor((rDxy-1)/2) + math.floor((xDxy -1)/2)
offsety = math.floor((rDxy-1)/2) + math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn + Lxy
#Bottom Left Box
magn = -1
offsetx = math.floor((rDxy-1)/2) + math.floor((xDxy -1)/2)
offsety = - math.floor((rDxy-1)/2) - math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn + Lxy
#Bottom Right Box
magn = 1;
offsetx = - math.floor((rDxy-1)/2) - math.floor((xDxy -1)/2)
offsety = - math.floor((rDxy-1)/2) - math.floor((yDxy -1)/2)
shiftX = math.floor((xDxy -1)/2)
shiftY = math.floor((yDxy -1)/2)
[ tsA,tsB,tsC,tsD ] = computeSs_Integral( intI, shiftX, shiftY, offsetx, offsety )
sA = unpad(tsA,pad)
sB = unpad(tsB,pad)
sC = unpad(tsC,pad)
sD = unpad(tsD,pad)
Lxy = (sD + sA - sB - sC) * magn + Lxy
R=np.multiply(Lxx,Lyy) - np.power((thresh*Lxy),2)
return R
In [29]:
R1= box_filters_criterion(n_img1,2.2)
R2= box_filters_criterion(n_img1,5.2)
R3= box_filters_criterion(n_img1,9.2)
f, (ax0,ax1,ax2) = plt.subplots(1, 3, figsize=(20, 10))
f.suptitle('Οπτικοποίηση κριτηρίου R για διάφορα scales (Βox-Filters Criterion)',fontsize=30)
ax0.imshow(R1,cmap='gray')
ax0.set_title("scale = 2 ",fontsize=20)
ax1.imshow(R2,cmap='gray')
ax1.set_title("scale = 5" , fontsize=20)
ax2.imshow(R3,cmap='gray')
ax2.set_title("scale = 9" , fontsize=20)
Out[29]:
